gerqf - Man Page

subroutine cgerqf (m, n, a, lda, tau, work, lwork, info)
CGERQF
subroutine dgerqf (m, n, a, lda, tau, work, lwork, info)
DGERQF
subroutine sgerqf (m, n, a, lda, tau, work, lwork, info)
SGERQF
subroutine zgerqf (m, n, a, lda, tau, work, lwork, info)
ZGERQF

CGERQF  

Purpose:

 CGERQF computes an RQ factorization of a complex M-by-N matrix A:
 A = R * Q.

Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

N

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit,
          if m <= n, the upper triangle of the subarray
          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
          if m >= n, the elements on and above the (m-n)-th subdiagonal
          contain the M-by-N upper trapezoidal matrix R;
          the remaining elements, with the array TAU, represent the
          unitary matrix Q as a product of min(m,n) elementary
          reflectors (see Further Details).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

TAU

          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).

WORK

          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
          For optimum performance LWORK >= M*NB, where NB is
          the optimal blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  The matrix Q is represented as a product of elementary reflectors

     Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).

  Each H(i) has the form

     H(i) = I - tau * v * v**H

  where tau is a complex scalar, and v is a complex vector with
  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

Definition at line 138 of file cgerqf.f.

DGERQF  

Purpose:

 DGERQF computes an RQ factorization of a real M-by-N matrix A:
 A = R * Q.

Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

N

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit,
          if m <= n, the upper triangle of the subarray
          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
          if m >= n, the elements on and above the (m-n)-th subdiagonal
          contain the M-by-N upper trapezoidal matrix R;
          the remaining elements, with the array TAU, represent the
          orthogonal matrix Q as a product of min(m,n) elementary
          reflectors (see Further Details).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

TAU

          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
          For optimum performance LWORK >= M*NB, where NB is
          the optimal blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  The matrix Q is represented as a product of elementary reflectors

     Q = H(1) H(2) . . . H(k), where k = min(m,n).

  Each H(i) has the form

     H(i) = I - tau * v * v**T

  where tau is a real scalar, and v is a real vector with
  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
  A(m-k+i,1:n-k+i-1), and tau in TAU(i).

Definition at line 138 of file dgerqf.f.

SGERQF  

Purpose:

 SGERQF computes an RQ factorization of a real M-by-N matrix A:
 A = R * Q.

Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

N

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

A

          A is REAL array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit,
          if m <= n, the upper triangle of the subarray
          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
          if m >= n, the elements on and above the (m-n)-th subdiagonal
          contain the M-by-N upper trapezoidal matrix R;
          the remaining elements, with the array TAU, represent the
          orthogonal matrix Q as a product of min(m,n) elementary
          reflectors (see Further Details).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

TAU

          TAU is REAL array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).

WORK

          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
          For optimum performance LWORK >= M*NB, where NB is
          the optimal blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  The matrix Q is represented as a product of elementary reflectors

     Q = H(1) H(2) . . . H(k), where k = min(m,n).

  Each H(i) has the form

     H(i) = I - tau * v * v**T

  where tau is a real scalar, and v is a real vector with
  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
  A(m-k+i,1:n-k+i-1), and tau in TAU(i).

Definition at line 138 of file sgerqf.f.

ZGERQF  

Purpose:

 ZGERQF computes an RQ factorization of a complex M-by-N matrix A:
 A = R * Q.

Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

N

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit,
          if m <= n, the upper triangle of the subarray
          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
          if m >= n, the elements on and above the (m-n)-th subdiagonal
          contain the M-by-N upper trapezoidal matrix R;
          the remaining elements, with the array TAU, represent the
          unitary matrix Q as a product of min(m,n) elementary
          reflectors (see Further Details).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

TAU

          TAU is COMPLEX*16 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
          For optimum performance LWORK >= M*NB, where NB is
          the optimal blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  The matrix Q is represented as a product of elementary reflectors

     Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).

  Each H(i) has the form

     H(i) = I - tau * v * v**H

  where tau is a complex scalar, and v is a complex vector with
  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

Definition at line 138 of file zgerqf.f.